Hamiltonian cycle complexity for solid hexagonal grids

Determine the computational complexity of the Hamiltonian Cycle Problem for solid hexagonal grid graphs.

Background

The related-work discussion contrasts the known complexity of Hamiltonian cycle problems on several grid families. Although the problem is known to be NP-complete for general hexagonal grids and polynomially solvable for solid triangular grids, the authors identify the corresponding complexity classification for solid hexagonal grids as unresolved.